This invention has one of its most important applications in measuring the motion error of the spindle of machine tools, although it has other applications as well. In today""s manufacturing world, high-speed machine tools with high feed rates and high-speed spindles are frequently required to deliver accuracy in the order of a few micrometers. It is important that the spindle error motion be measured and maintained to within the allowed tolerance.
Briefly, the major spindle motion error is caused by the lack of alignment of the spindle rotational axis, the centerline of the tool holder and the centerline of the tool. All of these should be coaxial. Any deviation from this coaxial relationship will generate eccentric motion error. Other causes of radial and axial error motions are the spindle bearings, structure error motion, etc as described in Ref. 1.
Conventional measurement techniques using a precision spindle tester, capacitor transducers and an oscilloscope are complex and heavy as described in References 1 and 2. The prior art precision spindle testers are very heavy and need periodic calibration. The capacitor transducers are limited by the sensitivity, range and non-linearity.
Disclosed here is a new non-contact method for the measurement of axis of rotation motion error for both 3 anad 5 axis machines. The accuracy and resolution are high, the range is large, and there is no need for a heavy precision spindle tester(see Reference 3). The present invention preferably uses a laser system previously used for the measurement of the static volumetric positioning accuracy (Ref. 4) and the dynamic contouring accuracy (Ref. 5), with some simple unique accessories and data analysis software to provide the measurement of spindle motion error and any axis of rotation motion error. The additional cost of the accessories and the software is low. Hence, it is cost effective and time saving. Furthermore, the heavy precision tester is no longer needed.
Thus, as compared with conventional techniques, among the advantages of the invention are: higher accuracy and resolution; larger standoff distance; easy setup and operation; no need for a heavy tester and periodical calibration; and cost and time savings
The application of this technique is not limited to spindle motion error determination; it can be applied to any axis of rotation spindle and other motion error. As above indicated, of perhaps less importance certain aspects of this invention have application in measuring the displacement motion of objects other than spindle motion.
The total spindle motion error at a constant rotational speed can be expressed as a function of the angle O within a single 360 degree rotation and the number of cycles i.
ri("THgr")=rf+dr("THgr")+dri("THgr"),i=1,2,3, . . . Nxe2x80x83xe2x80x83Eq. 1 
where rf is the fundamental error motion, dr("THgr") is the residual error motion, dri ("THgr") is the asynchronous error motion, "THgr" is the rotational angle, and N is the total number of cycles.
Here rf is due to the offset between the spindle axis of rotation and the center of the tool, dr("THgr") is due to the spindle bearing, the non-roundness of the sphere, and other synchronous error motion, and dri ("THgr") is due to the structure error motion or other asynchronous error motion. Once the total spindle error motion ri ("THgr") is measured, the rf, dr("THgr"), dri ("THgr") can be determined by the following relations:
rf= less than  less than ri(O) greater than i greater than oxe2x80x83xe2x80x83Eq. 2 
dr("THgr")= less than ri(O) greater than ixe2x88x92rfxe2x80x83xe2x80x83Eq. 3 
where  less than   greater than i=xcexa3i [ ]/N is the average over N cycles and  less than  greater than "THgr"=xcexa3o { }/2xcfx80is the average over 2xcfx80angle.
For machine tool applications, there is a sensitive direction of spindle motion, defined as that component of axis motion that occurs in a direction that is directly toward or away from a cutting tool. There are two types of sensitive directions, one is the fixed sensitive direction, in which the work-piece is rotated by the spindle and the point of machining is fixed such as a lathe. The other is the rotating sensitive direction, in which the work-piece is fixed and the point of machining rotates with the spindle such as a milling machine.
There are 6 degrees of spindle error motion. However, as discussed in Ref (2) only three of them are relevant. These are the radial error motion, tilt error motion and axial error motion. The radial error motion is the error motion in a direction normal to the z-axis. The tilt error motion is the error motion in an angular direction relative to the z-axis. The axial error motion is the error motion co-linear with the z-axis.
Let the laser measurement in the x-direction be xcex94X("THgr") and in the y-direction be xcex94Y("THgr"). For a fixed sensitive direction along the x-axis, the radial motion polar plot has the equation
r("THgr")=ro+xcex94X("THgr")xe2x80x83xe2x80x83Eq. 4 
where r0 is the base circle radius. For a rotating positive direction the radial motion is given by the equation
r("THgr")=r0+xcex94X("THgr")cos O+xcex94Y("THgr") sin Oxe2x80x83xe2x80x83Eq. 5 
In the analysis here, let the laser measurement in the x and y direction be
xcex94X("THgr")=A cos "THgr"+u("THgr")xe2x80x83xe2x80x83Eq. 6 
xcex94Y("THgr")=A sin "THgr"+v("THgr")xe2x80x83xe2x80x83Eq. 7 
where A is the offset between spindle axis of rotation and the center of the sphere, u("THgr") and v("THgr") are the error motion in the x- and y-direction respectively. Assume u("THgr") and v("THgr") are much smaller than A, the radial error motion can be expressed as
r("THgr")=SQRT[xcex94X("THgr")*xcex94X("THgr")+xcex94Y("THgr")*xcex94Y("THgr")]xe2x80x83xe2x80x83Eq. 8 
=A+u("THgr") cos ("THgr")+v("THgr") sin "THgr"xe2x80x83xe2x80x83Eq. 9 
This is similar to Eq. 5. For the fixed sensitive direction, the radial error motion can be expressed as
r("THgr")=xcex94X("THgr")xe2x80x83xe2x80x83Eq. 10 
=A cos "THgr"+u("THgr")xe2x80x83xe2x80x83Eq. 11 
To simplify the calculation, it sometimes can be assumed that the spindle error motion is axial symmetric. That is, the error motion measured in the x-direction is the same as measured in the y-direction shifted by 90 degree. Hence
xcex94X("THgr")=A cos "THgr"+u("THgr")xe2x80x83xe2x80x83Eq. 6 
xcex94Y("THgr")=A cos ("THgr"xe2x88x92xcfx80/2)+u("THgr"xe2x88x92xcfx80/2)xe2x80x83xe2x80x83Eq. 12 
=A sin O+v(O)xe2x80x83xe2x80x83Eq. 7 
where v("THgr")=u("THgr"xe2x88x92xcfx80/2) is a good approximation.
Hence, the radial error motion can be obtained by a laser measurement in the x-direction to be described.
The present invention, among other things, provides a method and means to measure displacement motion error of an object, such as a tool bit on the spindle of a 3 or 5 axis machine tool which spindle has either an intended fixed or variable spindle axis position, by the use of a curved, preferably spherically or cylindrically shaped beam energy reflecting surface attached to the end of the spindle. A source of beam energy, preferably a laser beam, is directed at this curved surface from a beam traverse distance measuring system like, for example, the single aperture laser head measuring apparatus disclosed in U.S. Pat. No. 5,116,126. The beam is initially directed toward what is assumed to be the nearest point on the reflecting surface where the beam would be reflected in the exact reverse direction from that of the incoming beam direction. Where this surface is a sphere or cylinder, the center of the sphere would be located where it is assumed the cutting point of the tool involved is to be located in the machine tool application of the invention.
If the beam direction is traverse to a rotating spindle, then any movement of the spindle which has a component traverse to the spindle axis will cause the beam to strike another portion of the curved reflecting surface further away from the previous point struck by the beam so that the beam is reflected at an angle to the incoming direction thereof. The distance traversed by the beam as measured by the beam traverse distance measuring apparatus involved, such as the laser head described in said patent, would be increased to a degree varying with the position of the curved surface struck by the beam relative to the closest position struck by the beam. To ensure that the reflected beam returns to the point of the measuring apparatus where it can be detected, a focusing lens can be placed between the measuring apparatus and the reflecting surface. As the spindle rotates, this measuring apparatus produces spindle motion error data which is a measure of the varying degrees to which the spindle undesirably wobbles in a direction transverse to its ideal stationary axis.
If the rotating spindle wobbles undesirably in an axial direction, any such axial movement will also vary the distance the beam traverses in the space between the measuring apparatus and the reflecting surface. In this example, this data is a measure of the spindle error motion along its axis. By using laser heads or the like directing their beams toward the reflecting surface along the x, y and z axes of the machine tool, the data developed by these laser heads represent the x, y and z axis motion errors for the sampling measuring times involved.
A 5-axis machine tool has a spindle with an inner portion which can be rotated, for example, about the z-axis and an inner portion which can either be aligned and fixed in position with respect to the inner portion of the spindle or, where the inner portion is not to be rotated, can be pivoted or rotated with respect to the inner portion of the spindle about either x or y axis directed axes of rotation. When the spindle axis of rotation is varied using any of these spindle rotation choices, error measurements like that just described with separate beam sources directing their beams along the x, y and z axes involved developes useful error motion data with which to evaluate the quality of the motion-imparting means involved.
Other aspects of the invention to be described in detail below include a unique test structure including a frame adjustably supporting the preferred spherical reflecting surface. A related aspect of the invention is the manner in which the position of the sphere is adjusted so that the center of the sphere which replaces the tool bit is located at the point where the cutting edge of the tool is to be located. The measurements referred to will then indicate the cutting tool motion error due to the undesired radial or angular wobblng of the spindle. Another aspect of the invention provides a visual presentation of the degree to which a rotating spindle having aligned inner and outer portions wobbles traverse to its axis of rotation. In this case, two laser head used simultaneously or one laser head used in sequence can direct laser beams respectively in x and y axis directions toward a spherical reflecting surface attached to the rotating spindle. The distance verses time data simultaneously developed by the lase head or heads which receive the reflected beams respectively produce sinusoidal and co-sinusoidal signals which when fed to the x and y axis inputs of a cathode ray tube or other similar display device produces a circular trace which shows the degree to which the spindle transversely wobbles during each revolution of the spindle at each of the angles involved.